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The octonion (Cayley) algebra is studied in a split basis by means of a formalism that brings outs its quark structure. The groups SO(8), SO(7), and G2 are represented by octonions as well as by 8 × 8 matrices and the principle of triality is studied in this formalism. Reduction is made through the physically important subgroups SU(3) and SU(2) ⊗ SU(2) of G2, the automorphism group of octonions.

It is shown that a Lorentz covariant coordinate~~ can be chosen in the case of the Kerr-Sch~ld. geometry which leads to the vanishing of the pseudo energy-mome~!um tensor and hence to the Imeanty of the Einstein equations. The ~etarded time and the reUlrded distance are introduced and the Lienard-Wiechert potentials are g~eraIized to gravitation in the case of world-line singularities to derive solutions of the ty~._~ of Bonnor and Vaidya. An accelerated version of the de Sitter metric is also obtained. Because of the Hneanty, complex translations can be performed on these solutions, resulting in a special relativistic version of the Trautman-Newman technique and Lorentz covariant solutions for spinning systems can be derived, including a new anisotropic interior metric that matches to the Kerr metric on an oblate spheroid.

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